They could.
Characters could even purchase medieval style armors and use those (though the Marshal will have to determine a cost). There are going to be social issues (lots of odd looks from townsfolk, suspicious guards and sheriffs wondering why you think you need that kind of protection, and a wealth of killers aiming for your limbs or noggin) but a character can do it.

But it's worth noting that just about every firearm has AP 1 or more. Heck, a common melee weapon (the bowie knife) has AP 1. Armor is great, but of very limited utility in the West, except when fighting monsters. _________________"Got a problem? I've got the solution: Rocket Launcher."
"Not against a Servitor."
"... We're all gonna die."

On the very first session of our campaign, after fighting a wallcrawler, the first thing the posse did was strip its hide and try to get a tanner in Dodge to make it into body armor. I shook my head and sadly mourned the D&D-ness of the situation, then went ahead and came up with stats for it. _________________My Blog: Jim - Yes, THAT Jim
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Armor went out of favor historically because musket balls and bullets just pierced right through light armor and wearing heavy armor didn't justify the lessened protection against bullets. As VahallaGH noted, pistols and bowie knives have AP1 (goes straight through leather armor) and rifles have AP 2 (goes straight through chain mail). Thus the only way to get any armor protection from bullets is to either strap on 40 lbs of plate mail (not to mention find someone who sells it) for a measly +1 protection, or pay the big bucks for a Smith & Robbards vest.

Or just get your posse's Huckster to cast Armor on you. That works just as well and you don't have to add the weight!_________________Wild Card Creator: Any PDF, Any Setting, No Extra Cost.

Now that I think about it, I imagine that would have the same effect as a plate corslet. Not bad against a pistol, less useful against a rifle, and heavy.

I'd submit that The Man With No Name took the time to find a piece that provided Heavy Armor - it was simply too thick for a normal bullet to overcome._________________"Got a problem? I've got the solution: Rocket Launcher."
"Not against a Servitor."
"... We're all gonna die."

Yep, that's one of the reasons it worked. He figured out a quirk of his foes and used it to his advantage. He didn't have to carry a lot of weight, just enough to cover the heart.

And (if it wasn't mentioned) there is one other form of armor in Deadlands. Check the first special ability under Rattlers in the Marshal's book. _________________Clint Black
Savage Worlds Core Rules Brand Manager